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It might be easier to get students to think about this by arranging it as a 1-D problem first. They seem to be distracted by unimportant elements of the problem, e.g., how they get to the final configuration.

It seems that the value of student discussion here is to stimulate thought and discussion about center of mass, and newton's laws outside the asymmetric context of gravity near the surface of the earth. Is there a way to stimulate this discussion in a shorter time. Can this activity be streamlined or is there some value I'm missing in their intellectual meandering?

It is interesting that the students don't think to impose a coordinates system when solving this problem. It seems that they are trying to generate an intuitive solution to the problem

This activity might be improved by using a computer simulation to enforce the rules of Newtonian Mechanics. In its current form, the only thing that enforces Newtonian Mechanics is the authority of the instructor.